Nonlinear Equations - UFRJ

Glossary of notations
As a general typographical convention, a stands for a scalar quantity,
a for a vectorial quantity, A for a matrix or operator or geometrical
entity, A for a space, A for a ring or algebra, a for an ideal.
I(X) – Ideal of polynomials vanishing at X 17
x L y – Group action: y = a(L, x). 19
Z(f) – Zero set. 21
F – Fewspace (Def. 5.2 or 5.15) or a product of. 56
V – Evaluation function associated to a fewspace. 56
K(x, y) – Reproducing kernel associated to a fewspace. 57
ω – Kähler form associated to a fewspace. 57
F x x – Fiber of f ∈ F with f(x) = 0. 58
dF – Zero average, unit variance normal probab. distrib. 62
P d – Space of polynomials of degree ≤ d in n variables. 63
P d – P d1 × · · · × P dn . 63
H d – Space of homog. polynomials of deg. d in n + 1 vars. 66
N(f, x) – Newton operator. 82
γ(f, x) – Invariant related to Newton iteration. 84
ψ(u) – The function 1 − 4u + 2u 2 . 88
β(f, x) – Invariant related to Newton iteration. 97
α(f, x) – Invariant related to Newton iteration. 97
173